Let $X = \operatorname{Spec}(R)$ be a conical Poisson variety over $\mathbb{C}$. This means that $R$ is a non-negatively graded Poisson algebra over $\mathbb{C}$ with $R_0 = \mathbb{C}$ and that the Poisson bracket is homogeneous of negative degree. Assume that $X$ admits a conical symplectic resolution. Examples to keep in mind are:

- the nilpotent cone in a simple Lie algebra
- a Slodowy slice to a nilpotent orbit inside the nilpotent cone
- the symmetric scheme of $n$ points on a Kleinian singularity
- a hypertoric variety
- a quiver variety.

Let $S$ be a symplectic leaf of $X$.

**Q: Is it possible for the fundamental group of $S$ to be infinite?**

In the first four examples listed above, the fundamental group of every symplectic leaf is finite. I don't know whether or not this property holds for quiver varieties, or for other examples.